Schwarzschild coordinates
E41074
Schwarzschild coordinates are a spherical coordinate system used in general relativity to describe the spacetime geometry outside a spherically symmetric, non-rotating mass, such as a static black hole.
Aliases (2)
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
coordinate system
→
general relativity concept → spherical coordinate system → |
| associatedWith |
Schwarzschild radius
→
Schwarzschild solution → event horizon of a Schwarzschild black hole → |
| assumes |
non-rotating central mass
→
spherical symmetry → static spacetime → |
| contrastsWith |
Kerr coordinates for rotating black holes
→
|
| describes |
Schwarzschild metric
→
exterior region of a static black hole → spacetime outside a spherically symmetric non-rotating mass → vacuum solution of Einstein field equations with spherical symmetry → |
| domainOfAzimuthalAngle |
0 ≤ φ < 2π
→
|
| domainOfPolarAngle |
0 ≤ θ ≤ π
→
|
| domainOfRadialCoordinate |
0 < r < ∞
→
|
| domainOfTimeCoordinate |
-∞ < t < ∞
→
|
| hasCoordinate |
r
→
t → θ → φ → |
| hasCoordinateSingularityAt |
Schwarzschild radius
→
|
| hasCoordinateType |
azimuthal angle φ
→
polar angle θ → radial coordinate r → time coordinate t → |
| hasLimitation |
breaks down at the event horizon
→
not regular across r = 2GM/c^2 → |
| hasLineElementForm |
ds^2 = -(1-2GM/r)c^2 dt^2 + (1-2GM/r)^{-1} dr^2 + r^2(dθ^2 + sin^2θ dφ^2)
→
|
| hasMetricSignature |
(-,+,+,+)
→
|
| hasPhysicalSingularityAt |
r = 0
→
|
| introducedInContextOf |
exact solutions of Einstein field equations
→
|
| mathematicallyDefinedOn |
Schwarzschild manifold
→
|
| namedAfter |
Karl Schwarzschild
→
|
| relatedTo |
Eddington–Finkelstein coordinates
→
Kruskal–Szekeres coordinates → isotropic coordinates → |
| usedFor |
calculating gravitational redshift
→
calculating light deflection by gravity → calculating perihelion precession → studying radial infall into a black hole → studying test particle orbits → |
| usedIn |
general relativity
→
|
| usedToDescribe |
gravitational field outside a non-rotating black hole
→
gravitational field outside a planet → gravitational field outside a star → |
| usesUnits |
geometrized units in many treatments
→
|
| validFor |
r greater than Schwarzschild radius
→
|
Referenced by (10)
| Subject (surface form when different) | Predicate |
|---|---|
|
Karl Schwarzschild
→
Karl Schwarzschild → |
knownFor |
|
Eddington–Finkelstein coordinates
→
Painlevé–Gullstrand coordinates → |
relatedTo |
|
Kruskal–Szekeres coordinates
→
|
basedOn |
|
Schwarzschild radius
→
|
coordinateSingularityAt |
|
Boyer–Lindquist coordinates
→
|
generalizes |
|
Karl Schwarzschild
→
|
hasConceptNamedAfter |
|
Reissner–Nordström metric
("Schwarzschild-like coordinates")
→
|
hasCoordinateSystem |
|
Painlevé–Gullstrand coordinates
("Schwarzschild radial coordinate")
→
|
hasSpatialCoordinates |